### 57435 results for qubit oscillator frequency

Contributors: Bertet, P., Chiorescu, I., Harmans, C. J. P. M, Mooij, J. E.

Date: 2005-07-13

**qubit** bias point ϵ by ± 2 G H z around 0 . The constants g 1 and g 2 are...**qubit** dephasing time as a function of $\delta \nu_0$. We discuss the specific...**frequency** in the figure). The dashed line indicates the phase-noise insensitive...**oscillator** variables coming from the flux-dependence of the SQUID Josephson...**qubit** is insensitive to the thermal fluctuations of the plasma mode (see...**qubits** is known to arise because of a variety of environmental degrees...**frequency** shift now depends on ϵ . Since g 2 is negative (see figure fig...high-**frequency** noise from the dissipative impedance. The SQUID is threaded...**Qubit** frequency ν q as a function of the bias ϵ for Δ = 5.5 G H z (minimum...**qubit**. Because of the coupling, the **qubit** frequency is shifted by an amount...**qubit**. Because of the coupling, the **qubit** **frequency** is shifted by an amount...flux-**qubit** is the loop in red containing the three junctions of phases...mode-**qubit** interaction hamiltonian which, in addition to the usual Jaynes-Cummings...flux-**qubit** coupled to the plasma mode of its DC-SQUID detector. We first...**qubit** biased by Φ x and SQUID biased by current I b . (b) Simplified electrical...**Frequency** shift per photon δ ν 0 as a function of I b and ϵ . The white...**Qubit** **frequency** ν q as a function of the bias ϵ for Δ = 5.5 G H z (minimum...**qubit** is effectively decoupled from the measuring circuit fluctuations...**qubit**-plasma mode coupling hamiltonian, we will neglect the admittance...SQUID-**qubit** system is seen as an inductance L J connected to the shunct...**qubit** is insensitive to phase noise (due to flux or bias current noise...flux-**qubit** coupled to a harmonic oscillator...SQUID-**qubit** coupling is not symmetric and the junctions critical current...**qubit** transition **frequency** ν q = Δ 2 + ϵ 2 . The corresponding dependence ... Decoherence in superconducting **qubits** is known to arise because of a variety of environmental degrees of freedom. In this article, we focus on the influence of thermal fluctuations in a weakly damped circuit resonance coupled to the **qubit**. Because of the coupling, the **qubit** **frequency** is shifted by an amount $n \delta \nu_0$ if the resonator contains $n$ energy quanta. Thermal fluctuations induce temporal variations $n(t)$ and thus dephasing. We give an approximate formula for the **qubit** dephasing time as a function of $\delta \nu_0$. We discuss the specific case of a flux-**qubit** coupled to the plasma mode of its DC-SQUID detector. We first derive a plasma mode-**qubit** interaction hamiltonian which, in addition to the usual Jaynes-Cummings term, has a coupling term quadratic in the **oscillator** variables coming from the flux-dependence of the SQUID Josephson inductance. Our model predicts that $\delta \nu_0$ cancels in certain non-trivial bias conditions for which dephasing due to thermal fluctuations should be suppressed.

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Contributors: Dutta, S. K., Strauch, Frederick W., Lewis, R. M., Mitra, Kaushik, Paik, Hanhee, Palomaki, T. A., Tiesinga, Eite, Anderson, J. R., Dragt, Alex J., Lobb, C. J.

Date: 2008-06-28

**qubit**. (a) The **qubit** junction J 1 (with critical current I 01 and capacitance...**qubit** interacting with an additional quantum system. It appears, though...**qubit** Hamiltonian and also compare time-dependent escape rate measurements...**frequency** detuning. Given the slightly anharmonic level structure of the...**oscillations** plotted in the time and **frequency** domains. (a) The escape...**oscillation** **frequencies** of Γ and ρ 11 are equal, even at high power in...**oscillation** **frequencies** with a simplified model constructed from the full...**qubit** junction. The measured escape rate shows Rabi **oscillations** followed...**oscillation** of 1 , which is why we believe the **frequency** analysis in Fig...**qubit** with a 100 um^2 area junction acquired over a range of microwave...**oscillation** **frequencies** Ω R , 0 1 m i n and Ω R , 0 2 m i n and (b) ...**qubit**, measured at 20 mK. The scatter in the values is indicative of the...**oscillations** followed by a decay governed by multiple time constants. ...two-**qubit** experiments; the second SQUID was kept unbiased throughout the...**Qubit** energy-level spectroscopy and tunneling escape rates. (a) Open circles...**qubit** junction are analogous to those of a ball in a one-dimensional tilted...**qubit** dynamics, particularly at high power. To investigate the effects...**frequency**, and leakage to the higher excited states....**qubit**...**qubit** junction, this was taken as the microwave amplitude I r f t . For...**oscillation** **frequency** Ω R , 0 1 at fixed bias as a function of microwave...**qubit** junction was itself calibrated by the observed oscillation frequency...**oscillation** **frequency** increases with power and decoherence causes the ...**oscillation** **frequencies** in ways that are in quantitative agreement with ... We present Rabi **oscillation** measurements of a Nb/AlOx/Nb dc superconducting quantum interference device (SQUID) phase **qubit** with a 100 um^2 area junction acquired over a range of microwave drive power and **frequency** detuning. Given the slightly anharmonic level structure of the device, several excited states play an important role in the **qubit** dynamics, particularly at high power. To investigate the effects of these levels, multiphoton Rabi oscillations were monitored by measuring the tunneling escape rate of the device to the voltage state, which is particularly sensitive to excited state population. We compare the observed **oscillation** **frequencies** with a simplified model constructed from the full phase **qubit** Hamiltonian and also compare time-dependent escape rate measurements with a more complete density-matrix simulation. Good quantitative agreement is found between the data and simulations, allowing us to identify a shift in resonance (analogous to the ac Stark effect), a suppression of the Rabi **frequency**, and leakage to the higher excited states.

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Contributors: Wallquist, M., Shumeiko, V. S., Wendin, G.

Date: 2006-08-09

**qubit** 1, and Hadamard gates H are applied to the second **qubit**....**qubits** at their optimal points with respect to decoherence during the ...**oscillator** is entangled with **qubit** 1, at the next resonance the **oscillator**...**qubit**-cavity resonances compared to the differences in the **qubit** frequencies...**qubit** states is achieved by sweeping the cavity frequency through the **qubit**-cavity resonances. The circuit is scalable, and allows to keep the...**qubit**-**qubit** coupling and simple gate operations. Tunable **qubit**-cavity ...**oscillator** with variable **frequency**. Our goal in this section will be to...**qubit** 2 and ends up in the ground state. A Bell measurement is performed...**frequency** is sequentially swept through resonances with both **qubits**; at...**qubit** coupling to a distributed **oscillator** - stripline cavity possesses...**qubit** states is achieved by sweeping the cavity **frequency** through the **qubit**-cavity resonances. The circuit is scalable, and allows to keep the...**qubit** 2 before swapping its state back onto **qubit** 1; free evolution during...**qubit**-cavity resonances compared to the differences in the **qubit** **frequencies**...two-**qubit**-cavity system, and analyze appropriate circuit parameters. We...**oscillators** represents the stripline cavity, φ 1 and φ N are superconducting...**qubits** via tunable stripline cavity...**qubit** eigenbasis), which is achieved for the charge **qubits** biased at the...**qubit**-**qubit** coupling strength is smaller than the on-resonance coupling...**qubits** **frequency** asymmetry and the coupling **frequency**. Recent suggestions...**qubits**; at the first resonance the oscillator is entangled with **qubit** ...two-**qubit** operation. The **qubits** coupled to the cavity must have different...**qubit** 1 swaps its state onto the **oscillator**, then the **oscillator** interacts...**qubits** mediated by a superconducting stripline cavity with a tunable resonance...**oscillator** through resonance with both **qubits** performing π -pulse swaps...**frequency**. The **frequency** control is provided by a flux biased dc-SQUID...**qubits**, and projecting on the **qubit** eigenbasis, | g | e , by measuring ... We theoretically investigate selective coupling of superconducting charge **qubits** mediated by a superconducting stripline cavity with a tunable resonance **frequency**. The **frequency** control is provided by a flux biased dc-SQUID attached to the cavity. Selective entanglement of the **qubit** states is achieved by sweeping the cavity **frequency** through the **qubit**-cavity resonances. The circuit is scalable, and allows to keep the **qubits** at their optimal points with respect to decoherence during the whole operation. We derive an effective quantum Hamiltonian for the basic, two-**qubit**-cavity system, and analyze appropriate circuit parameters. We present a protocol for performing Bell inequality measurements, and discuss a composite pulse sequence generating a universal control-phase gate.

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Contributors: Altomare, Fabio, Cicak, Katarina, Sillanpää, Mika A., Allman, Michael S., Sirois, Adam J., Li, Dale, Park, Jae I., Strong, Joshua A., Teufel, John D., Whittaker, Jed D.

Date: 2010-02-02

**qubit** when its **frequency** is far from the cavity's resonant **frequency**. ...**qubit** when its frequency is far from the cavity's resonant frequency. ...**qubit** as function of superconducting phase difference ϕ across the JJ ...**qubits**. The left ordinate displays the **oscillation** **frequency** as determined...**qubit** and the resonant **frequency** in the left well ( N l ) as a function...**qubit**, (b) the CPW cavity, (c) the second **qubit**. (Red): ϕ 1 = 0.8949 ϕ...**qubit** behavior that agrees well with the experimental data. These results...**qubit** transfers part of its energy to the CPW cavity. The second **qubit**...**qubit** (or CPW cavity) capacitance, L i the geometrical inductance, L j...**qubit** is measured, the superconducting phase can undergo damped **oscillations**...**qubit** 2 (**qubit** 1) by performing a Gaussian fit of N l versus flux (or ...**oscillation** is large, the **frequency** of the **oscillations** is lower than ...**qubits**. The left ordinate displays the resonant **frequency** as measured ...**frequency** of **oscillation** in the right well matches the CPW cavity resonant...**oscillation** in right well matches the CPW cavity resonant **frequency** and...**qubits** coupled by a resonant coplanar waveguide cavity. After the first...**qubit** 2, after **qubit** 1 has already tunneled as function of the (dimensionless...**qubit** **frequency**. As the system loses energy due to the damping, the **oscillation**...**qubit**, is maximum at a flux ϕ 2 / ϕ c 2 ∼ 0.837 , where the second **qubit**...**qubits** coupled by a coplanar waveguide...**frequency** chirped noise signal whose **frequency** crosses that of the cavity...**qubits** can be reduced by use of linear or possibly nonlinear resonant ...**qubit** states | 0 if the **qubit** did not tunnel and | 1 if the **qubit** did ...**qubit**(classically) undergoes damped **oscillations** in the anharmonic right...**qubit** is measured, the superconducting phase can undergo damped oscillations...**oscillator**). C i is the total i - **qubit** (or CPW cavity) capacitance, L...**qubit** 1 (**qubit** 2). Notice that the crosstalk transferred to **qubit** 2 (**qubit** ... We analyze the measurement crosstalk between two flux-biased phase **qubits** coupled by a resonant coplanar waveguide cavity. After the first **qubit** is measured, the superconducting phase can undergo damped **oscillations** resulting in an a.c. voltage that produces a **frequency** chirped noise signal whose **frequency** crosses that of the cavity. We show experimentally that the coplanar waveguide cavity acts as a bandpass filter that can significantly reduce the crosstalk signal seen by the second **qubit** when its **frequency** is far from the cavity's resonant **frequency**. We present a simple classical description of the **qubit** behavior that agrees well with the experimental data. These results suggest that measurement crosstalk between superconducting phase **qubits** can be reduced by use of linear or possibly nonlinear resonant cavities as coupling elements.

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Contributors: Cooper, K. B., Steffen, Matthias, McDermott, R., Simmonds, R. W., Oh, Seongshik, Hite, D. A., Pappas, D. P., Martinis, John M.

Date: 2004-05-31

**qubit** well is much shallower and state | 1 rapidly tunnels to the right...**qubit** in state | 0 (solid circles) and in an equal mixture of states |...**oscillations** is consistent with the spectroscopic splittings observed ...**qubits** and microscopic critical-current fluctuators by implementing a ...**qubit**'s resonant frequency. The results point to a possible mechanism ...**oscillation** periods are observed to correspond to the spectroscopic splittings...**qubit** circuitry. For the **qubit** used in Fig. 2, the Josephson critical-current...**qubit**'s resonant **frequency**. The results point to a possible mechanism ...**qubit** probability amplitude first moves to state | 1 g and then oscillates...**oscillations** between Josephson phase **qubits** and microscopic critical-current...**qubit** and a microscopic resonator using fast readout...**qubit** probability amplitude first moves to state | 1 g and then **oscillates**...**qubit** with strength h S / 2 . On resonance, the **qubit**-fluctuator eigenstates...**qubits** and demonstrate the means to measure two-**qubit** interactions in ...**qubit** spectroscopy near Δ U / ℏ ω p = 3.55 , showing splittings of strengths ... We have detected coherent quantum **oscillations** between Josephson phase **qubits** and microscopic critical-current fluctuators by implementing a new state readout technique that is an order of magnitude faster than previous methods. The period of the **oscillations** is consistent with the spectroscopic splittings observed in the **qubit**'s resonant **frequency**. The results point to a possible mechanism for decoherence and reduced measurement fidelity in superconducting **qubits** and demonstrate the means to measure two-**qubit** interactions in the time domain.

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Contributors: Chirolli, Luca, Burkard, Guido

Date: 2009-06-04

**qubit** states $|0>$ and $|1>$ during measurements. Our theory can be applied...**qubit** in the state "0" vs driving time τ 1 and τ 2 , at Rabi **frequency**...**qubit** surrounded by a SQUID. b) Measurement scheme: b1) two short pulses...**qubit** state is extracted from the **oscillator** measurement outcomes, and...**qubit**-shifted **frequencies**, Δ ω ≈ ± g . For weak driving amplitude f , ...**oscillator** driving amplitude is f / 2 π = 20 ~ G H z and a damping rate...**qubit** QND measurement is studied in the regime of strong projective **qubit**...**qubit** current states is made small compared to the **qubit** gap E = ϵ 2 +...**qubit** is coupled to a harmonic oscillator which undergoes a projective...**oscillator** at resonance with the bare harmonic **frequency**, Δ ω = 0 . The...**qubit**-dependent "position" x s are shown in the top panel. Fig2...**qubit**-split **frequencies**, that is enhanced when the driving strength f ...**qubit** in a generic state. Here, ϵ and Δ represent the energy difference...**frequency** ϵ 2 + Δ 2 , before and between two measurements prepare the ...**qubit**-shifted **frequency**....**qubit** state is extracted from the oscillator measurement outcomes, and...**qubit** measurement. Two mechanisms lead to deviations from a perfect QND...**oscillator** to a **qubit**-dependent state. c) Perfect QND: conditional probability...**qubit** turns out to be quadratic. The **qubit** Hamiltonian is H S = ϵ σ Z ...**qubit** is coupled to a harmonic **oscillator** which undergoes a projective...**oscillator** is driven at resonance with the bare harmonic **frequency** and...**qubit** relaxation time T 1 = 10 ~ n s is assumed. Fig1...**qubit**) and quantify the degree to which such a **qubit** measurement has a...**qubit**-shifted **frequencies**, the probability has a two-peak structure whose...**qubits** coupled to a circuit **oscillator**....**qubit** state and measurement outcomes and a weak **qubit** measurement....**oscillator**, and (ii) quantum tunneling between the **qubit** states $|0>$ ...**qubit**-dependent....**qubit** driving time τ 1 and τ 2 starting with the **qubit** in the state | ...**qubit** coupled to a harmonic oscillator ... We theoretically describe the weak measurement of a two-level system (**qubit**) and quantify the degree to which such a **qubit** measurement has a quantum non-demolition (QND) character. The **qubit** is coupled to a harmonic **oscillator** which undergoes a projective measurement. Information on the **qubit** state is extracted from the **oscillator** measurement outcomes, and the QND character of the measurement is inferred by the result of subsequent measurements of the **oscillator**. We use the positive operator valued measure (POVM) formalism to describe the **qubit** measurement. Two mechanisms lead to deviations from a perfect QND measurement: (i) the quantum fluctuations of the **oscillator**, and (ii) quantum tunneling between the **qubit** states $|0>$ and $|1>$ during measurements. Our theory can be applied to QND measurements performed on superconducting **qubits** coupled to a circuit **oscillator**.

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Contributors: Il'ichev, E., Oukhanski, N., Izmalkov, A., Wagner, Th., Grajcar, M., Meyer, H. -G., Smirnov, A. Yu., Brink, Alec Maassen van den, Amin, M. H. S., Zagoskin, A. M.

Date: 2003-03-20

**qubit**) , inductively coupled to a high-quality superconducting tank circuit...**Qubit**...**oscillations**....**qubit** increasing the tank’s linewidth ; these are inconsequential for ...**qubit**, and simultaneously as a filter protecting it from noise in the ...**frequency** ω T . That is, while wide-band (i.e., fast on the **qubit** time...**qubit** through a separate coil at a frequency close to the level separation...**qubit**, coupled to a high-quality tank circuit tuned to the Rabi **frequency**...**oscillations** in time. We report evidence for such **oscillations** in a _continuously...**qubit** modifying the tank’s inductance and hence its central frequency,...**qubit** is effectively decoupled from the tank unless it **oscillates** with...**qubit** **frequency**, confirm that the effect is due to Rabi **oscillations**. ...**qubit**, coupled to a high-quality tank circuit tuned to the Rabi frequency...**qubit** has L q = 24 pH; the larger junctions have C q = 3.9 fF and I c ...**frequency** of the tank is measured as a function of HF power....**qubit** is inductively coupled to a tank circuit. The DC source applies ...**qubit** modifying the tank’s inductance and hence its central **frequency**,...**qubit** in the classical regime ....**qubit** through a separate coil at a **frequency** close to the level separation...**qubit** quality factor \~7000....**qubit** inside the Nb pancake coil....**qubit** is effectively decoupled from the tank unless it oscillates with ... Under resonant irradiation, a quantum system can undergo coherent (Rabi) **oscillations** in time. We report evidence for such **oscillations** in a _continuously_ observed three-Josephson-junction flux **qubit**, coupled to a high-quality tank circuit tuned to the Rabi **frequency**. In addition to simplicity, this method of_Rabi spectroscopy_ enabled a long coherence time of about 2.5 microseconds, corresponding to an effective **qubit** quality factor \~7000.

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Contributors: Saiko, A. P., Fedaruk, R.

Date: 2010-12-10

**qubits** arises at double resonance in a bichromatic field when the **frequency**...**frequency** equals the Larmor **frequency** of the initial **qubit**. We show that...**Qubits** in a Doubly Resonant Bichromatic Field...**qubit** operations in the strong-field regime, the counter-rotating component...radio-**frequency** (rf) field is close to that of the Rabi **oscillation** in...**qubit** and transitions created by a bichromatic field at double resonance...**qubits** can be selected by the choice of both the rotating frame and the...**qubits** arises at double resonance in a bichromatic field when the frequency...**qubit**. We show that the operational multiphoton transitions of dressed ... Multiplication of spin **qubits** arises at double resonance in a bichromatic field when the **frequency** of the radio-**frequency** (rf) field is close to that of the Rabi **oscillation** in the microwave field, provided its **frequency** equals the Larmor **frequency** of the initial **qubit**. We show that the operational multiphoton transitions of dressed **qubits** can be selected by the choice of both the rotating frame and the rf phase. In order to enhance the precision of dressed **qubit** operations in the strong-field regime, the counter-rotating component of the rf field is taken into account.

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Contributors: Strauch, F. W., Dutta, S. K., Paik, Hanhee, Palomaki, T. A., Mitra, K., Cooper, B. K., Lewis, R. M., Anderson, J. R., Dragt, A. J., Lobb, C. J.

Date: 2007-03-02

**frequency**, and two-photon Rabi **frequency** are compared to measurements ...**frequency** Ω R , 01 of the one-photon 0 1 transition as function of microwave...**qubit**, scanned in **frequency** (vertical) and bias current (horizontal). ...**qubit** (current-biased Josephson junction) at high microwave drive power...**qubit** with Nb/AlOx/Nb tunnel junctions. Good agreement is found between...**oscillations** of the escape rate for I a c = 16.5 nA....**oscillations** have been observed in many superconducting devices, and represent...**oscillation** **frequency** Ω ̄ R , 01 as a function of the level spacing ω ...**qubit**...**qubit**, scanned in frequency (vertical) and bias current (horizontal). ...**qubits**) in a quantum computer. We use a three-level multiphoton analysis ... Rabi **oscillations** have been observed in many superconducting devices, and represent prototypical logic operations for quantum bits (**qubits**) in a quantum computer. We use a three-level multiphoton analysis to understand the behavior of the superconducting phase **qubit** (current-biased Josephson junction) at high microwave drive power. Analytical and numerical results for the ac Stark shift, single-photon Rabi **frequency**, and two-photon Rabi **frequency** are compared to measurements made on a dc SQUID phase **qubit** with Nb/AlOx/Nb tunnel junctions. Good agreement is found between theory and experiment.

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Contributors: Averin, D. V.

Date: 2002-02-05

**qubit**. The oscillations are represented as a spin rotation in the z - ...**qubit**, σ z and σ y , as required in the QND Hamiltonian ( 2). For discussion...**oscillations** avoiding the detector-induced dephasing that affects the ...**frequency** Δ . QND measurement is realized if the measurement frame (dashed...**qubit** structure that enables measurements of the two non-commuting observables...**oscillations** in an individual two-state system. Such a measurement enables...**qubits** which combine flux and charge dynamics....**frequency** Ω ≃ Δ ....**qubit**...**oscillations** of a **qubit**. The **oscillations** are represented as a spin rotation ... The concept of quantum nondemolition (QND) measurement is extended to coherent **oscillations** in an individual two-state system. Such a measurement enables direct observation of intrinsic spectrum of these **oscillations** avoiding the detector-induced dephasing that affects the standard (non-QND) measurements. The suggested scheme can be realized in Josephson-junction **qubits** which combine flux and charge dynamics.

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